Largest Euler characteristic of a downset on an n-dimensional cube.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =6a(5) =10a(6) =15a(7) =35a(8) =70a(9) =126a(10) =210a(11) =462a(12) =924a(13) =1716a(14) =3003a(15) =6435a(16) =12870a(17) =24310a(18) =43758a(19) =92378a(20) =184756a(21) =352716a(22) =646646a(23) =1352078a(24) =2704156a(25) =5200300a(26) =9657700a(27) =20058300a(28) =40116600a(29) =77558760